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I read somewhere that if you place an elongated geostationary satellite tangential to the Earth it will rotate so that its long axis is in line with the radius. Presumably, as soon as one end goes slightly inside of the tangent it is fractionally heavier and the opposite end lighter which then is reinforced. what is this called/where can I find out more?

user36093
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This is tidal or gravity gradient stabilization, and works due to the point closer to earth having slightly more attractive force due the inverse square law so will tend towards vertical given time. The effect is not restricted to geostationary orbit.

GremlinWranger
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